+91-87964 74404
FlagBACK
Question icon
Grade 11Analytical Geometry

pn is the ordinate of any point p on the parabola y^2=4x. if the normal at p to the parabola its axis at g then find ng.

Profile image of supraja venkatraman
7 Years agoGrade 11
Answers icon

1 Answer

Profile image of kkbisht
7 Years ago
Equation of normal at P (t2,2t) ( a parametric coordinate of a parabola y2=4x with vertex at origin) is given by  y +tx=2t+t3  Now this normal  meets the axis of parabola ( Y=0 ) at  0+tx=2t+t3 => x=2+t2 ( cancelling t)  .This is the point g i.e. og=2+t2 and the ordinate of the point P is 2t and the x-cordinte is t2 i.e on=t2  ( o is the origin as well as vertex of the parabola) therefore ng=og-on=2+t2-t2=2
therefore the length ng=2
 
kkbisht

Other Related Questions on analytical geometry

question mark
  • The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is 
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius. 
 
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
1 Answer Available

Last Activity: 4 Years ago